The adaptive perturbation method decomposes a Hamiltonian by the diagonal elements and nondiagonal of Fock state. state are solvable but can contain information about coupling constants. We study harmonic oscillator with interacting potential, [Formula: see text], where text] constants, is position operator. In this study, each perturbed term has an exact solution. demonstrate accurate spectrum...

The adaptive perturbation chooses a non-standard decomposition. Hamiltonian becomes sum of solvable and parts. We calculate the spectrum using method at leading-order to compare numerical solutions. maximum deviation is around 5% for different coupling regions. A study relies on whether choice suitable. Our result with parameters should show that provides appropriate saddle points all In end, w...

this paper presents the high order frequency-amplitude relationship for nonlinear transversely vibrating beams with odd and even nonlinearities using homotopy perturbation method with an auxiliary term (hpmat). the governing equations of vibrating buckled beam, beam carrying an intermediate lumped mass and quintic nonlinear beam are investigated to exhibit the reliability and ability of the pro...

in this paper, homotopy perturbation method (hpm) has been applied to investigate the effect of magnetic field on cu-water nanofluid flow in non-parallel walls. the validity of hpm solutions were verified by comparing with numerical results obtained using a fourth order runge–kutta method. effects of active parameters on flow have been presented graphically. the results show that velocity in bo...

In this paper, we consider the inhomogeneous time-fractional nonlinear Fisher equation with three known boundary conditions. We first apply a modified Homotopy perturbation method for translating the proposed problem to a set of linear problems. Then we use the separation variables  method to solve obtained problems. In examples, we illustrate that by right choice of source term in the modified...